---
title: "Capture effect; gain parameter of DSB-FC envelope detection"
subject: "Communication Systems"
chapter: 9
key: "semester_6/communication_systems:capture-effect-dsbfc-envelope-gain"
source: https://www.bctengineer.com/q/semester_6/communication_systems/capture-effect-dsbfc-envelope-gain
site: BCT Engineering
---

# Capture effect; gain parameter of DSB-FC envelope detection

Communication Systems · Chapter 9: Noise in Communication Systems

- Asked in: 2070 Asar (CS II), 2+5 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/capture-effect-dsbfc-envelope-gain
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-9

## Question

What is capture effect? Calculate the gain parameter in DSB-FC with envelope detection.

## Short answer

Capture effect is the FM receiver property that the stronger of two nearly identical frequency signals is reproduced and the weaker is almost completely suppressed. The DSB-FC envelope-detection gain parameter is γ = k_a²P/(1 + k_a²P); for tone modulation γ = μ²/(2 + μ²). At 100% modulation (μ = 1) γ = 1/3.

## Answer

#### Capture effect

**Capture effect** is the property of an FM receiver whereby, when two FM signals on (nearly) the same frequency are received, the **stronger one is reproduced and the weaker one is almost completely suppressed**. The limiter and discriminator respond to the dominant signal's phase, so the weaker signal appears only as small noise. If the two strengths are nearly equal (within about 1 dB), the receiver may switch between them. AM receivers do not show this; both signals are heard together.

#### Gain parameter (figure of merit) of DSB-FC with envelope detection

**Assumptions:** message $m(t)$ of bandwidth $W$ and power $P = \overline{m^2(t)}$; white noise of PSD $N_0/2$; IF filter bandwidth $2W$; high carrier-to-noise ratio.

Transmitted signal: $s(t) = A_c[1 + k_a m(t)]\cos\omega_c t$

**Channel (input) SNR.** Signal power $= \dfrac{A_c^2(1+k_a^2P)}{2}$; noise power in bandwidth $W$ (reference baseband) $= WN_0$:

$$
(SNR)_C = \frac{A_c^2(1+k_a^2P)}{2WN_0}
$$

**Received signal with narrowband noise**

$$
\begin{aligned}
x(t) &= [A_c + A_ck_am(t) + n_I(t)]\cos\omega_c t - n_Q(t)\sin\omega_c t
\end{aligned}
$$

where $n_I, n_Q$ each have power $2WN_0$. The envelope is

$$
y(t) = \sqrt{[A_c + A_ck_am(t) + n_I(t)]^2 + n_Q^2(t)}
$$

For high SNR, $A_c[1+k_am(t)] \gg |n_Q(t)|$, so

$$
y(t) \approx A_c + A_ck_am(t) + n_I(t)
$$

The DC term $A_c$ is removed by a blocking capacitor.

**Output SNR**

$$
(SNR)_O = \frac{A_c^2k_a^2P}{2WN_0}
$$

**Figure of merit (gain parameter)**

$$
\gamma = \frac{(SNR)_O}{(SNR)_C} = \frac{k_a^2P}{1+k_a^2P}
$$

which is always **less than 1**.

**Single tone** $m(t) = A_m\cos\omega_m t$, $\mu = k_aA_m$: $k_a^2P = \mu^2/2$, so

$$
\gamma = \frac{\mu^2}{2+\mu^2}
$$

For 100 % modulation ($\mu = 1$): $\gamma = 1/3$. So DSB-FC with envelope detection needs **three times (4.77 dB) more** transmitted power than DSB-SC/SSB with coherent detection ($\gamma = 1$) for the same output SNR, because much power goes into the carrier.

**Low SNR:** when noise dominates the carrier, the message is no longer separable in the envelope and output SNR falls sharply: this is the **threshold effect** of the envelope detector.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. In capture effect, when two FM signals on the same frequency are received, the receiver
   A. reproduces both equally
   B. reproduces the stronger one and suppresses the weaker
   C. reproduces the weaker one only
   D. outputs only noise always
   Answer: B. The limiter and discriminator respond to the dominant signal's phase, so the weaker signal is almost entirely suppressed. (Key point: Capture effect)

2. The figure of merit of DSB-FC with envelope detection at high SNR is
   A. 1
   B. k_a^2 P / (1 + k_a^2 P)
   C. 1 + k_a^2 P
   D. 2 k_a^2 P
   Answer: B. SNR_o = A_c^2 k_a^2 P/(2WN_0) divided by SNR_C = A_c^2(1 + k_a^2 P)/(2WN_0). (Key point: Gain parameter of DSB-FC)

3. For a single tone at mu = 1, the gain parameter of DSB-FC envelope detection is
   A. 1
   B. 1/2
   C. 1/3
   D. 2/3
   Answer: C. gamma = mu^2/(2 + mu^2) = 1/3 at mu = 1. (Key point: Single tone at 100% modulation)

4. Why does DSB-FC with envelope detection need about three times more power than DSB-SC for the same output SNR?
   A. It uses twice the bandwidth
   B. Much of the transmitted power is in the carrier, which carries no message
   C. The envelope detector adds extra noise power
   D. The message has lower power
   Answer: B. The carrier term consumes power but does not contribute to output SNR, so gamma is at most 1/3. (Key point: Why DSB-FC is less efficient)

## Related in Communication Systems

- [Threshold effect in envelope detection of DSB-FC](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Athreshold-envelope-dsbfc) — Communication Systems, chapter 9
- [Detection gains of DSB-FC, DSB-SC and SSB](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adetection-gain-dsbfc-dsbsc-ssb) — Communication Systems, chapter 9
- [Noise performance of coherent DSB-FC detection](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adsbfc-noise-coherent-100pct) — Communication Systems, chapter 9
- [Detection gain of SSB-SC vs DSB-SC](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adetection-gain-ssbsc-dsbsc) — Communication Systems, chapter 9, asked 2×
- [Detection gain of DSB-AM is less than 1](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adetection-gain-dsbam-less-than-1) — Communication Systems, chapter 9
- [Envelope detector; can it demodulate DSB-SC?](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aenvelope-detector-dsbsc) — Communication Systems, chapter 2, asked 2×